In this paper, we propose a new framework to provide continuous services to users by a collection of mobile servers distributed over an interconnection network. We model those mobile servers as a subset of host computers, and assume that a user host can receive the service if at least one adjacent host computer (including itself) plays the role of a server; i.e., we assume that the service could not be routed via the interconnection network. The main results obtained in this paper are summarized as follows: For the class of trees with n hosts, ⌈(n+1)/2⌉ mobile servers are necessary and sufficient to realize continuous services by the mobile servers, and for the class of Hamiltonian graphs with n hosts, ⌈(n+1)/3⌉ mobile servers are necessary and sufficient.